Pith Number

pith:7ZXXRC7H

pith:2018:7ZXXRC7HMOO652PPZDIVT27K47

not attested not anchored not stored refs pending

Planarity of Cayley graphs of graph products of groups

Olga Varghese

arxiv:1809.07997 v2 · 2018-09-21 · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZXXRC7HMOO652PPZDIVT27K47}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:52:33.799335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe6f788be7639deee9efc8d159ebeae7c0ba4a29ca53417ba2b144d3417e3847

Aliases

arxiv: 1809.07997 · arxiv_version: 1809.07997v2 · doi: 10.48550/arxiv.1809.07997 · pith_short_12: 7ZXXRC7HMOO6 · pith_short_16: 7ZXXRC7HMOO652PP · pith_short_8: 7ZXXRC7H

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7ZXXRC7HMOO652PPZDIVT27K47 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fe6f788be7639deee9efc8d159ebeae7c0ba4a29ca53417ba2b144d3417e3847

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ced352d4e847a9ee55f172017f90a2404e7383bf10a9ebe3d40c9f3c0224217",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-09-21T09:18:56Z",
    "title_canon_sha256": "0d631629cf6c222e61a0d5ea87e0a3a592d0b52b6d008c5f46f5244a996bc3ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07997",
    "kind": "arxiv",
    "version": 2
  }
}